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This problem involves using the **binomial probability formula** because we're calculating the probability of a certain number of successes (in this case, adults who do not need vision correction) in a fixed number of trials (7 adults).

Given the problem:

- Probability of an adult not requiring vision correction (\(p\)) = 0.21
- Number of trials (\(n\)) = 7
- We want to find the probability that exactly 2 of them do not require vision correction, so \(k = 2\).

The binomial probability formula is:

\[
P(X = k) = \binom{n}{k} \cdot p^k \cdot (1-p)^{n-k}
\]

Where:
- \(\binom{n}{k}\) is the binomial coefficient (the number of ways to choose \(k\) successes from \(n\) trials),
- \(p^k\) is the probability of exactly \(k\) successes,
- \((1-p)^{n-k}\) is the probability of the remaining trials being failures.

Now, let's calculate it.The probability that exactly 2 out of 7 randomly selected adults do not require vision correction is **0.285** (rounded to three decimal places).

Would you like more details or have any questions?

Here are five related questions to expand on this topic:

1. How would the probability change if we were interested in exactly 3 adults not requiring vision correction?
2. What is the probability that none of the 7 adults require vision correction?
3. How can we calculate the expected number of adults who do not require vision correction out of 7?
4. What is the probability that at least 1 adult out of 7 does not require vision correction?
5. How would the problem change if the probability of not requiring vision correction was 50%?

**Tip:** In binomial distributions, the mean (expected value) is given by \(n \cdot p\), which can help anticipate results!

Assume that when an adult is randomly selected, the probability that they do not require vision correction is 21%. If 7 adults are randomly selected, find the probability that exactly 2 of them do not require vision correction.

This problem involves calculating the binomial probability that exactly 2 out of 7 adults do not require vision correction, with the probability of no vision correction being 21%. Learn how to apply the binomial probability formula to solve this question.

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